From: Marielouise (for Teacher2Teacher Service)
Date: Apr 02, 2000 at 22:20:07
Subject: Re: Apothems of polygon activities

I have done a search on the math forum library and lesson plans and have
found nothing.  The apothem of a regular polygon is the radius of the
inscribed circle.  You might consider having students draw fairly large
figures and then construct the Incenter, the center of the inscribed circle.
In a triangle, you find the Incenter by bisecting the angles of the figure.
Dropping the altitude from the Incenter to any side gives the length of the
apothem or radius of the inscribed circle.   In regular polygons with even
number of sides, draw the diagonals and the INcenter is where the diagonals
intersect.  In a regular polygon with an odd number of sides, again bisect
the angles.  What the students should observe is the angle bisectors/diagonal
divide the regular polygon into congruent triangles.  Again the apothem is
the altitude of the triangle from the vertex at the Incenter to the opposite
side.

 -Marielouise, for the Teacher2Teacher service

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